Pith Number

pith:F5OYLZCC

pith:2015:F5OYLZCC7QUSQGHYUFRTVVVQZM

not attested not anchored not stored refs pending

BMO: Oscillations, self improvement, Gagliardo coordinate spaces and reverse Hardy inequalities

Mario Milman

arxiv:1505.02633 v3 · 2015-05-11 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F5OYLZCC7QUSQGHYUFRTVVVQZM}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:37:01.473510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f5d85e442fc292818f8a1633ad6b0cb00a76c91d899f66f8851df7e64d8d95f

Aliases

arxiv: 1505.02633 · arxiv_version: 1505.02633v3 · doi: 10.48550/arxiv.1505.02633 · pith_short_12: F5OYLZCC7QUS · pith_short_16: F5OYLZCC7QUSQGHY · pith_short_8: F5OYLZCC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/F5OYLZCC7QUSQGHYUFRTVVVQZM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2f5d85e442fc292818f8a1633ad6b0cb00a76c91d899f66f8851df7e64d8d95f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72b30209aebd11218dadc527b2dd83cf439280251477bb3a09ce93fd1a1f0c2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-05-11T14:13:37Z",
    "title_canon_sha256": "a5ef6dfabb68665d65ed803f46cd532372a88a5dac63377abfd19298404e66c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02633",
    "kind": "arxiv",
    "version": 3
  }
}